1. Algebra 2 Solving Radical Equations Section 7-5 Solving Square Root and Other Radical Equations Lesson 7-5

2. Algebra 2 Objectives To solve radical equations To solve problems containing radicals Solving Square Root and Other Radical Equations Lesson 7-5

3. Algebra 2 The Principle of Powers For any natural number n, if a = b is true, then a n = b n is true. Solving Square Root and Other Radical Equations Lesson 7-5

4. Algebra 2 Solve and Check Solving Square Root and Other Radical Equations Lesson 7-5

5. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

6. Algebra 2 Solve Radical Equations ISOLATE a radical term on one side of the equation. USE the PRINCIPLE OF POWERS. SOLVE for ‘x’. CHECK your answer with original equation. Solving Square Root and Other Radical Equations Lesson 7-5

7. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

8. Algebra 2 –10 + 2x + 1 = –5 Solve –10 + 2x + 1 = –5. Solving Square Root and Other Radical Equations Lesson 7-5 2x + 1 = 5 Isolate the radical. ( 2x + 1 ) 2 = 5 2 Square both sides. 2x + 1 = 25 2x = 24 x = 12 Check: –10 + 2x + 1 = –5 –10 + 2(12) + 1 –5 –10 + 25 –5 –10 + 5 –5 –5 = –5 Additional Examples

9. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

10. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5 Solve 3(x + 1) = 24. 3535 x + 1 = 32Simplify. x = 31 3(x + 1) = 24 3535 (x + 1) = 8Divide each side by 3. 3535 Check: 3(x + 1) = 24 3(31 + 1) 24 3(2 5 ) 24 3(2) 3 24 24 = 24 3535 3535 3535 3535 5353 ((x + 1) ) = 8 Raise both sides to the power. 5353 5353 (x + 1) 1 = 8 Multiply the exponents and. 5353 5353 3535 Additional Examples

11. Algebra 2 Extraneous Roots Sometimes a solution to the equation that resulted from squaring both sides is not a solution of the original equation. That number is called an extraneous root. Solving Square Root and Other Radical Equations Lesson 7-5

12. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5 Solve x + 2 – 3 = 2x. Check for extraneous solutions. x + 2 – 3 = 2x x + 2 = 2x + 3Isolate the radical. ( x + 2) 2 = (2x + 3) 2 Square both sides.0 = 4x 2 + 11x + 7Combine like terms. 0 = (x + 1)(4x + 7)Factor. x + 2 = 4x 2 + 12x + 9Simplify. x + 1 = 0 or 4x + 7 = 0Factor Theorem x = –1 orx = – 7474 Additional Examples

13. Algebra 2 Check: x + 2 – 3 = 2x x + 2 – 3 = 2x –1 + 2 – 3 2(–1) + 2 – 3 2 1 – 3 –2 – 3 –2 = –2 – 3 7272 – 7474 – 1414 1212 7272 – 7272 – = – 5252 / 7474 – Solving Square Root and Other Radical Equations Lesson 7-5 (continued) The only solution is –1. Additional Examples

14. Algebra 2 Homework Page 388 # 1-19 odd, Skip 13

15. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5 Solve (x + 1) – (9x + 1) = 0. Check for extraneous solutions. 2323 1313 x = 0 or x = 7 (x + 1) 2 = 9x + 1 x 2 + 2x + 1 = 9x + 1 x 2 – 7x = 0 x(x – 7) = 0 (x + 1) – (9x + 1) = 0 2323 1313 (x + 1) = (9x + 1) 2323 1313 ((x + 1) ) 3 = ((9x + 1) ) 3 2323 1313 Additional Examples

16. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5 (continued) Check: (x + 1) – (9x + 1) =0 (x + 1) – (9x + 1) = 0 (0 + 1) – (9(0) + 1) 0(7 + 1) – (9(7) + 1) 0 (1) – (1) 0 (8) – (64 ) 0 (1) – (1 2 ) 0 (8) – (8 2 ) 0 1 – 1 = 0 8 – 8 = 0 2323 1313 2323 1313 2323 1313 2323 1313 2323 2323 2323 1313 2323 1313 2323 1313 2323 1313 2323 2323 Both 0 and 7 are solutions. Additional Examples

17. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

18. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

19. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

20. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

21. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

22. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

23. Algebra 2 Solving Square Root and Other Radical Equations Lesson 7-5

24. Algebra 2